Verity Jones kindly provided a soap box for me to compare the theories of Nikolov & Zeller to those of “Climate Scientists” exemplified by Scott Denning. If N&Z are right the huge sums of money governments around the world are committing to “Mitigating” CO2 emissions can have no effect on global temperature.

In the discussion that followed supporters of Scott Denning were asked to provide an equation expressing the relationship between atmospheric CO2 and global temperature. David Appell was bold enough to take the challenge by citing Arrhenius’ 1896 paper. Arrhenius makes the counter intuitive assertion that minor components of the atmosphere such as water vapor and CO2 overwhelm the effect of the bulk of our atmosphere:

“The selective absorption of the atmosphere is……………..not exerted by the chief mass of the air, but in a high degree by aqueous vapor and carbonic acid, which are present in the air in small quantities.”

Arrhenius goes on to develop a relationship between CO2 concentration and global temperature as summarized in his “Table VII” predicting the variation of temperature (oC) as a function of CO2 concentration:

The Arrhenius figures are in italics. A weighted average has been calculated that follows the function shown above. “A” in the above table represents the concentration of CO2 as a ratio to 280 ppm (the approximate CO2 concentration in 1896). The Arrhenius theory is elegant in its simplicity and it is still the theoretical basis for the “Catastrophic Anthropogenic Global Warming” theory. Let’s take a closer look at what it implies.

With the benefit of hindsight we can test Arrhenius’ predictions against the observed warming from 1896 to the present. According to NCDC the average global temperature increased 0.7 K compared withΔT = 5.43 log(2) (395/280) = 2.7 K. The Arrhenius prediction is not even close but there are other problems.

The trouble with “Halving”

The Arrhenius theory can be used to predict the effect of high or low CO2 concentrations. Arrhenius’ specific predictions are shown in blue while halvings are shown in yellow. In 1896, Earth’s atmosphere contained ~2,200 Giga-tonnes of CO2, so 20 halvings would reduce this to about 2 million tonnes which means it would take another 115 halvings to get down to just one CO2 molecule.

At that point the temperature would be over 400 Kelvin below absolute zero. As this is a physical impossibility the Arrhenius theory fails this sanity test. While one can excuse Arrhenius for overlooking this, modern “Climate Scientists” should have either abandoned the Arrhenius’ theory or modified it to address this issue.

The trouble with “Doubling”

According to James Hansen, adding CO2 to the atmosphere will cause a “Runaway Greenhouse Effect”. After 18.3 “Doublings” the partial pressure of CO2 on Earth would be identical to the surface pressure on Venus. In Fig. 1, the corresponding “Delta T” is 99 K above the 1896 value of 287 K = 386 K. While this sounds pretty scary, it is far short of the observed surface temperature on Venus which is ~350 K higher. A spectacular “Fail” for James Hansen.

The temperature increase predicted by the Arrhenius theory can be expressed as a “Forcing” in Watts per square meter. While the sun delivers about 1,367 W/m2 only half of the planet is illuminated at any given moment and over 30% of the incoming radiation is reflected. The average power absorbed is ~345 W/m2.

After ten doublings the partial pressure of CO2 would be 0.29 bars and the forcing would be ~345 W/m2, equal to the solar radiation absorbed at Earth’s surface. This would imply that all the outgoing “Thermal Infra-Red” had been captured by the CO2 and returned to the surface. This is not physically possible so it seems that the doubling effect also fails another sanity test. Once again one can excuse Arrhenius but not modern “Climate Scientists”. In fact the maximum amount of outgoing radiation that can be captured by CO2 and returned to the surface is ~15 Watts/m2 as explained in the “Unified Theory of Climate Revisited”.

Arrhenius updated

Thanks to satellites and modern instrumentation climate scientists such as Scott Denning have access to more accurate data than was available in 1896. Consequently, the modern estimate of the effect of a “Doubling” is ~1.2 Kelvin instead of the 5.4 K assumed by Arrhenius. See Fig. 3.

As mentioned earlier the global average temperature has risen by ~0.7 K since 1896. Back then there was ~280 ppm of CO2 in the atmosphere compared to 395 ppm today. Using the formula ΔT = 1.2 log(2) (395/280) the warming should be 0.6 K, in reasonable agreement with observations. So far so good for Denning but things got worse for Hansen’s “Runaway Greenhouse Effect”. After 18.3 doublings (to 93 Atm.) the predicted warming is only 22 K for a temperature of 309 K. For comparison the N&Z pressure based theory predicts a surface temperature of 628 K on Earth at the same pressure compared with 739 K on Venus.

Here is another “Sanity Check” for the Denning theory. The Vostok ice cores show wide temperature excursions as the planet experienced a series of glaciations over the last 700,000 years. Currently, Earth is enjoying an “Inter-Glacial” with temperatures about 10 K higher than at the peak of the last glaciation. Twenty thousand years ago the temperature was 10 K lower than today. Arrhenius wanted to explain “Ice Ages” in terms of CO2:

“….one might in this way probably find an explanation for temperature variations of 5o-10o C.”

If there was any validity to Fig. 3 the CO2 concentration would have been 8 halvings lower than today or 1 part per million. The Vostok ice cores show that the CO2 concentration never fell below 190 ppm. This failure is beyond spectacular.

Discussion

No matter whether one takes the Arrhenius idea in its original or updated form it does not come close to explaining observations on Earth or Venus. The theory fails a string of sanity checks and yet scientists around the world act as if it had some validity.

It is puzzling that theories based on thermodynamics explain observations with good precision yet they receive little attention. In 1969 Carl Sagan’s correctly predicted the surface temperature of Venus by applying the concept of “Adiabatic Lapse Rate” from the cloud tops down to the surface. More recently N&Z’s 2011 “Unified Theory of Climate” has accurately predicted surface temperatures on many planets and moons.

My conclusion is that it does not matter what the science says when politics and money dominate.

108 Responses to Arrhenius Revisited

Peter, your “20 halvings” calculation may be the most absurd, dumbest thing I’ve ever seen a [snip] do — and that’s saying a lot.

I’m beginning to see that your real problem is that you apply equations without understanding them — without looking at what their assumptions are and how they are derived. That’s always a mistake in physics, and you make some whoppers.

Everyone knows Arrhenius’s climate sensitivity was too high, that there are issues with his model. That’s the point of making a model: to make better models. As modelers say, “All models are wrong, but some are useful.” Arrhenius’s genius is that he made a wrong but useful model.

It’s like you are using the Bohr model of the atom to show that lasers couldn’t possibly work. Everyone knows the Bohr model wasn’t the last word in atomic theory. But it was a great start. So what’s the point of beating a dead horse?

In my earlier post I said:
“Thus far I have been unable to find a clear mathematical explanation from “Consensus Scientists” to show how CO2 accounts for a GHE of 33 Kelvin. There is a good reason for this; it simply can’t be done. It is not possible to make the Arrhenius theory or its modern variants match observations.”

A more general version is in Pierrehumbert’s textbook, section 4.2: “Basic Formulation of Plane-Parallel Radiative Transfer.” There and in later sections he gives solutions to the equations in some simplified cases.

For the Earth’s real atmosphere, the equations are too complicated to be solved analytically, because of the complicated structure of the absorption spectrum of GHGs in the infrared, and the not-so-simple structure of the atmosphere, and so they are solved numerically.

But by all means, please go ahead and try to solve them analytically — you will win an immediate Nobel Prize. You might start by showing us what equation you’re using for the absorption spectrum — all the dumb scientists have to use the HITRAN database of spectroscopic measurements.

Peter’s own work hasn’t risen to the level that a mathematical debunking is necessary (or worth wasting time on). Wolfgang Pauli used to say that bad ideas were “not even wrong.” This falls into that class, and then some.

David,
The halving and doubling in the article above is a model. As you say: all models are wrong but some are useful. This model was used to show that Arrhenius’s estimate was too high, which you just agreed with. So the model is useful. But some models you throw sticks and stones at and some models you don’t. Why?

Are you using the correct value for Arrhenius’s prediction – he modified it in 1906 after criticism by Anstrom:

“In his 1896 publication Arrhenius asserted that a doubling of the CO2 level would increase the world’s average temperature by 5 to 6°C, with the high latitudes increasing more and the tropics less. Other scientists, such as the Swedish scientist Knut Angstrom, objected to the value that Arrhenius had used as the absorption coefficient for CO2. At the time Angstrom made his objection of the quantitative accuracy of the absorption coefficient (1900) Arrhenius rejected it, but by 1906 Arrhenius gave a revised estimate of the effect of a doubling of CO2 being 1.2°C directly and 2.1°C with the water vapor feedback effect included. Thus Arrhenius had acknowledged that he had overestimated the impact of a doubling of CO2 by about two hundred and fifty to three hundred percent. This overestimate had to have come largely, if not exclusively, from an overestimate of the absorption coefficient for carbon dioxide.”http://www.applet-magic.com/arrhenius.htm

I think you have it right. CO2 has an absorption band around 4.5 microns but water vapor absorbs in that region and it is usually present in much larger concentrations. David Appell supplied a chart that illustrates this very well:

That places a low limit on the “Forcing” that CO2 can deliver. The only band where it can plausibly have any effect is from 13.5 to 17 microns (wave numbers 580 to 750).

When you realize that the total forcing due to CO2 cannot exceed 15 Watts/square meter it should be obvious that the “Doubling” idea is absurd, whether you try 5.4°C/doubling (Arrhenius) or 1.2°C/doubling (Denning).

Peter, again: there is very little water vapor at higher altitudes, but lots of CO2. Have you included that fact in your analysis? If not your analysis is false.

“A related saturation fallacy, also popularized by Ångström, is that CO2 could have no influence on radiation balance because water vapor already absorbs all the IR that CO2 would absorb. Earth’s very moist, near-surface tropical atmosphere is nearly saturated in that sense, but the flaw in Ångström’s argument is that radiation in the portion of the spectrum affected by CO2 escapes to space from the cold, dry upper portions of the atmosphere, not from the warm, moist lower portions. Also, as displayed in the inset to figure 2, the individual water-vapor and CO2 spectral lines interleave but do not totally overlap. That structure limits the competition between CO2 and water vapor.”
– R Pierrehumbert, Physics Today, Jan 2011http://geosci.uchicago.edu/~rtp1/papers/PhysTodayRT2011.pdf

Angstrom pointed out that one of the strong absorption bands for CO2 coincides with absorption bands for water vapor. Peter Azlac’s explanation of Angstrom’s position is correct. Arrhenius responded to the criticism by reducing his 5.4°C/doubling estimate.

I thought you’re someone who likes a calculation. So where is your calculation showing this?

Pierrehumbert does address Angstrom’s issue: saturation is a fallacy. There is essentially no water vapor above the tropospause, so whatever IR gets through the water vapor [i.e. whatever water vapor radiates from its upper regions] can still be blocked above the tropospause. Thus CO2 can still have a large effect if its absorption band overlaps that of water vapor.

For a measurement showing that this is indeed happening, at least for clear sky conditions (i.e no clouds) see

They used satellites to measure less heat escaping out to space, at the particular wavelengths at which CO2 and CH4 and other GHGs absorb radiation. This outgoing radiation is decreasing, and at the wavelengths predicted by greenhouse gas theory — just as expected since we are adding greenhouse gases to the atmosphere:

By the way, if the CO2 wasn’t there, the Earth’s surface would be much, much colder. Water vapor itself doesn’t provide a sufficient greenhouse effect to change the bare blackbody temperature (255 K) to above freezing. It is only CO2 that, by its additional greenhouse effect, raises the surface temperature above 273 K (freezing) and enables there to be lots of water vapor in the atmosphere. See:

David,
Even if the ability of CO2 in the thermal IR had any relevance to establishing a temperature gradient in the troposphere (the adiabatic lapse rate), that gas cannot return more than 15 Watts/square meter to the ground. I call this a “Saturation” problem because the doubling idea implies much larger forcings than that.

Fig 2. shows the forcing for 10 doublings as ~345 Watts/m2 or 100% of the ground radiation so there is a need to correct the Arrhenius’ equation so that it can pass this simple sanity check.

Scott Denning proposes 1.2°C/doubling but that does not eliminate the saturation issue. Ten doublings would correspond to a 12°C temperature rise so instead of 288 K we would have 300 K. The forcing to bring this about would be {(300/288)^4-1}*345 = 61Watts/m2.

As I have told you elsewhere that Lacis paper is wrong and I would be happy to go into greater detail on your blog if you promise not to censor my comments.

With regard to the Harries paper, I have been trying to avoid discussing water vapor at all. In an earlier “Guest Post” on DITC there was a thought experiment that was specifically designed to avoid the need to talk about the effect of water in its various forms.

Peter wrote: “After 18.3 “Doublings” the partial pressure of CO2 on Earth would be identical to the surface pressure on Venus. In Fig. 1, the corresponding “Delta T” is 99 K above the 1896 value of 287 K = 386 K.”

This is a completely absurd and amateurish conclusion.

You simply cannot extrapolate over such huge scales while ignoring all the other changes that would necessarily take place.

As CO2 increases and the temperature goes up, atmospheric water vapor increases. But, in real life, at some point (on Earth) it rains out.

Look at your number: 386 K. That’s above the boiling point of water! The oceans would have boiled away and all the water would be in the atmosphere. There, like happened on Venus, UV radiation broke apart water molecules high in the atmosphere and the hydrogen was lost to space. After that point there can be no more water on Venus, so CO2 can’t be taken up in rocks via the Urey reactions. So the CO2 stays in the atmosphere, providing a large greenhouse effect.

David said:
“Your scenario boils off the Earth’s water. (In actuality that can’t happen on Earth because our solar irradiance is too low)….”

You believe Hansen’s scary fairy stories but never ask him to show his equations. Hansen says that rising CO2 could cause a “Runaway Greenhouse Effect” on Earth. If Fig 1. was correct he would be right but that plot is based on Arrhenius’ 5.4°C/doubling which is universally rejected.

Take a look at Fig 3. that is based on1.2°C/doubling and you will see that 18.3 doublings would raise the pressure to 93 bars while raising the temperature only 23°C (to 36°C). That falls well short of Hansen’s predictions that do include boiling oceans.

The Arrhenius conjecture is falsified by Figs 1 through 3. Can you tweak the doubling equation to make it fit observations? Certainly I can’t but you may know someone who can.

I will write a critique of that Lacis paper and attempt to post it on your blog.

As a journalist you probably took courses in rhetoric. Consequently, you use rhetoric (“comical and completely inept.”) when equations and reasoning would be more appropriate.

That is a VERY big if. The amount of coal on the planet is estimated to be 98.6e17 g C (Swart and Weaver, Nature Climate Change, 2012). That’s 10,000 gigatonnes of carbon! — we have emitted only 380 GtC so far from burning fossil fuels.

No one knows for sure what would happen if we burned that much carbon — there are simply no models that can go there. Hansen, who made his bones studying Venus, has earned his opinion on this subject in a way that few can match.

Besides, Arrhenius’ result might have been too high, but his model was a major advance and forms the basis for models today. As modelers say, “All models are wrong, but some are useful.” Arrheniius’s model, like Bohr’s, was very, very useful.

You keep writing “Scott Denning.” It’s not his equation, but has been around for a long time.

CO2 can’t explain the GHE, the PETM or Ice Age cycles.

In fact, none of these can be explained without the greenhouse effect (and, in the case of the PETM, then some). The greenhouse effect explains Venus’s high temperature, too.

What are you trying to accomplish here Peter? You clearly have some underlying need to deny the greenhouse effect. What is that about? Are you worried you might have to pay a little extra for gasoline and heating oil?

It’s utterly absurd to think that you (or N&K) have found something simple that 200 years of physicists have somehow missed. They thought of all these things decades and decades ago, and eliminated them as possible explanations, for reasons that aren’t that hard to understand. (Just look at the Earth’s outgoing spectrum.)

Do you think that if you just keep denying CO2’s properties it all will just go away? I honestly can’t understand your motivation.

David Appell said:
“It’s utterly absurd to think that you (or N&K) have found something simple that 200 years of physicists have somehow missed.”

The physics is really simple. The temperature gradient in the atmosphere (Adiabatic Lapse Rate) was something taught in my high school. The ADR rate correctly explains the GHE on Earth while theories based on the radiative properties of CO2 don’t.

Why do you say “You clearly have some underlying need to deny the greenhouse effect.” when I tell you “ad nauseam” that the GHE is real but much larger than 33 K?

Sagan correctly calculated the surface temperature on Venus by extrapolating the ADR from the cloud tops to the surface. Hansen on the other hand cannot explain the Venusian surface temperature using mathematics. All he has is rhetoric and fairy stories.

The ADR of Titan and Jupiter were measured using parachute probes. In each case the observed ADR is within 0.1 K/km of the theoretical value.

I honestly can’t understand your motivation for clinging to Arrhenius when his theory cannot explain observations.

Given the clear evidence in favor of the conjecture that the main bulk of the atmosphere causes the GHE it should not surprise you that N&K have been able to develop a “Unified Theory of Climate” that depends on total gas pressure rather than trace gases.

I explained why Gavin’s plot of the “Thermal IR” emitted from this planet has a “hole” at 15 microns. I told you that the same reasoning could be applied to oxides of Nitrogen, Ozone and Methane but not to water vapor.

While water vapor is a significant component of the atmosphere in the troposphere it is much less significant in the stratosphere owing to the phase change that occurs at zero deagrees Celsius. The zero of the Celsius scale is defined by the freezing point of water.

You are emotionally bound against the greenhouse effect, for some reason. This is a scientific travesty of the first order. Real scientists want to know and understand natural phenomena, not dismiss those they don’t like.

You don’t want to understand anything. You want to do cartoon physics, all while ignoring any result that does not agree with your comical worldview.

I’ve tried — as someone who knows a lot more science than you do, and has the degrees to prove it — to teach you a little physics.

You are clearly too old to learn much, if anything.

Your silly beliefs do not matter. The world has accepted the consequences of CO2 pollution, and knows it must cut its emissions.

You’re swatting against the wind, as I’m sure that you know, deep down. Keep doing your pretend, cartoon physics. Keep ignoring the hard questions. It only makes you look like a dummy.

You clearly have some underlying need to deny the greenhouse effect.” when I tell you “ad nauseam” that the GHE is real but much larger than 33 K?

Yes, Nikolov says it’s 133 K. From WUWT:
“If, as Nikolov claims, the Atmosphere boosts the surface temperature by 133K, then, absent the Atmosphere the Earth would be 288K – 133K = 155K. This is contradicted by the fact that the Moon, which has no Atmosphere and is at the same distance from the Sun as our Earth, has an average temperature of about 250K. Yes, the albedo of the Moon is 0.12 and that of the Earth is 0.3, but that difference would make the Moon only about 8K cooler than an Atmosphere-free Earth, not 95K cooler! Impossible!”http://wattsupwiththat.com/2011/12/29/unified-climate-theory-may-confuse-cause-and-effect/

Not to even mention that the silly N&K formula (2) considers the energy flux from empty space (their constant “cs,”), but ignores the interior heat of a body.

Space at 2.72 K radiates at 3 microW/m2.

But the Earth’s interior puts out 45 terrawatts, which is 90 milliW/m2.

So they consider one energy flux that is utterly negligible, while ignoring another that is 30,000 times larger. This is just one small problem with their scam.

David,
The albedo of the Earth is around 0.3 owing to clouds and ice caps while Venus with its 100% cloud cover has a Bond albedo of ~0.7. Lacking clouds or ice fields the albedo of the Moon is ~0.1.

N&K say that lacking an atmosphere Earth would have the same average temperatures as the Moon or 154 K. I don’t entirely agree because they have ignored the effect of the different rates of rotation. The Earth rotates 30 times faster than the Moon.

With regard to internal heat sources, N&K’s paper says nothing about this but I encountered the problem when I tried to apply their equations to the gas giants. In my opinion it makes no difference whether the heat comes from the Sun or from inside the planetary body. Heat from the planetary cores of Earth or Venus is tens of milli-Watts per square meter so you can safely ignore it when calculating an energy balance.https://diggingintheclay.wordpress.com/2012/03/13/unified-theory-of-climate/

I don’t know how you get the idea that N&K are performing a “Scam”. They have put forward a theory that explains observations much better than the “Climate Science” based on Arrhenius’ absurd conjecture. If you disagree with them you can point out errors in their equations or cite measurements that disprove what they say. That is what I have been trying to do with no success thus far.

Because:
(a) their hypothesis does not predict the correct temperature for the moon, while mine does, and
(b) THEIR HYPOTHESIS DOES NOT CONSERVE ENERGY! The Earth’s surface radiates infrared radiation, which does not interact with the N2 and O2 molecules of the atmosphere. (It does very slightly, but not by any mechanism you’ve ever suggested, and the interaction, called collision induced absorption, is very small.) This radiation simply passes through a classical atmosphere, except for water vapor, and water vapor doesn’t come close to explaining the observed enhanced surface temperatures. (Measurements for clear sky conditions show this explicitedly.)

As I’ve said many times now, the surface radiates at 390 W/m2, and the TOA at 240 W/m2. So where is the missing 150 W/m2?

You say that the average temperature is 213 K but the Diviner website says 206 K at the equator and 98 K at the poles. If you average over all latitudes the answer has got to be less than 160 K. I tried to calculate my own average by downloading the Diviner “Level 3” data but my spreadsheet choked. Thus I made my admittedly outrageous guess of 156 K.

N&K can’t even predict the temperature of the moon, which is about as simple a case of radiative transfer as exists. Standard theory predicts it exactly — it predicts the average, AND IT PREDICTS THE SHAPE AND MAGNITUDE OF THE CURVE FOR ALL EQUATORIAL LONGITUDES.

And just to bring this to completeness, the average depends on the temperature of the dark side of the moon, which no radiative theory can calculate because that number depends on heat conduction through the lunar regolith.

Measurements from Diviner shows it to be about 95 K, and using that number gives my average of 212 K. It’s not exactly constant, as Vasavada shows

a slight discrepency that accounts for the difference between Diviner’s number and Vasavada’s number.

Thanks for admitting that Scott Denning’s formula is wrong for the Moon. You are not correct when you say Denning’s 255 K is “equilibrated by an atmosphere”. The Earth would need to be a thermal superconductor to maintan a constant temperature from equator to pole.

The Diviner folks say the equatorial average temperature for the Moon is 206 K. You say that the average temperature for the entire Moon including the polar latitudes (average temperature 98 K) is 213 K. You are entitled to your opinion but I will go with the Diviner observations until something better shows up.

As noted several times the Diviner observations show that the lunar average temperature is less than 160 K. I still cannot get my spreadsheet to digest the Diviner data so I made an outrageous guess of 156 K. My guess makes a lot more sense than your 213 K or Scott Dening’s 255 K.

You are not correct when you say Denning’s 255 K is “equilibrated by an atmosphere”. The Earth would need to be a thermal superconductor to maintan a constant temperature from equator to pole.

I am correct. The assumption behind the formula’s derivation is that the body’s surface temperature is the same everywhere. It’s not a bad assumption; the average annual values vary only by about 10% across the Earth’s surface.

It’s an ASSUMPTION, made (as always in physics) as a compromise between what’s accurate and what’s calculatable. It gives a value for the GHE that is pretty good — within a few Kelvin of a much more robust calculation like Lacis et al.

You say that the average temperature is 213 K but the Diviner website says 206 K at the equator and 98 K at the poles.

My number, like Vasavada’s and like JPL’s, is for the equatorial average. My formula works at each point on the equator and agrees with Vasavada’s data.

There is no sunlight incident at the lunar poles, because there sunlight come in parallel to the tangent of the surface. Hence the value is the value from regolith conductance, 95 K. The same value holds everywhere on the circle dividing the lunar dayside from the nightside.

Lacis, Gavin et al. say that the radiative forcing on Venus is 16,000 watts/sq. meter whereas it is zero. They published that fiction, duly peer reviewed in ‘Science’ and you can find it referenced at the NASA GISS web site.

If you wanted a perfect example of the corrupt state of climate science in general and GISS in particular that paper is the poster child. To call those people “Scientists” dishonors the rest of us.

It’s atmosphere is 96.5% CO2. Since it’s at very high pressure (Ps=92 bars), pressure broadening of the absorption lines is huge — that is, the width of the absorption frequencies is very high — and very little IR radiation from the surface gets back out.

(Pressure broadening is also important for Mars, but for the other reason: there is little of it, since for Mars Ps=6 mb. Mars is also colder, so it radiates at higher wavelengths than Earth (its peak wavelength is 13.8 microns compared to Earth’s 10.1 microns), so less IR in the CO2 absorption range.)

Thanks for that Pierrehumbert comment; it is indeed very enlightening. He is discussing one of the problems with the Arrhenius “Doubling” idea. There has to be a lower limit to the process of doubling. I call this the “Saturation” problem. It is absurd to suggest that doubling from one molecule of CO2 to two for the entire planet Earth will have the same effect (a temperature increase of 1.2 K) as increasing today’s 3,000 Giga-tonnes to 6,000 Giga-tonnes.

At higher pressures the “Doubling” idea has such a feeble impact that it can’t come close to explaining the observed surface temperatures on Mars, Venus or Earth. This is the fundamental problem with the IPCC’s climate models that are unconvincing at “Backcasting” and laughable when it comes to forecasting even seven years into the future.

Today Mars has a surface pressure of ~685 Pascals. Imagine raising the pressure to 1 bar. That would be 7.19 doublings @ 0.91 K/doubling for a total of 6.5 K. Pressing on to match the Venusian atmospheric pressure would require another 6.54 doublings for 6.0 K. Thus with CO2 in the driver’s seat the surface temperature rises from 218K (600 Pascals) to 225 K (1 bar) and to 231 K (93 bars). What do N&K say? They predict temperatures of 233 K (1 bar) and 511 K (93 bar).

On Earth, starting at today’s ~390 ppm, raising the partial pressure of CO2 to 93 bars would correspond to 18.3 “Doublings”. According to Denning, Lacis, Schmidt and many others each doubling would increase the surface temperature by 1.2 K for a total of 22 K, corresponding to 310 K @ 93 bar. N&K predict a surface temperature of 630 K @ 93 bar but then the oceans would be converted into steam so you would have to add another 320 bars. N&K predict a surface temperature of 1200 K @ 413 bar. There would be no coming back from that “Runaway Greenhouse Effect”.

It is absurd to suggest that doubling from one molecule of CO2 to two for the entire planet Earth will have the same effect (a temperature increase of 1.2 K) as increasing today’s 3,000 Giga-tonnes to 6,000 Giga-tonnes.

It is indeed absurd, which is why Pierrehumbert makes no such claim; instead, he writes, “…To get a logarithmic behavior, you need enough pressure or temperature to make the lines broad enough to start overlapping.”

Once again you have scored an “Own Goal”. It seems that you do not support the Arrhenius theory after all:
“The selective absorption of the atmosphere is……………..not exerted by the chief mass of the air, but in a high degree by aqueous vapor and carbonic acid, which are present in the air in small quantities.”

You are implying (without any equations) that the bulk of the atmosphere is causing the warming by broadening the absorption lines of CO2!

On Earth, starting at today’s ~390 ppm, raising the partial pressure of CO2 to 93 bars would correspond to 18.3 “Doublings”. According to Denning, Lacis, Schmidt…

This is utterly amateurish claim. Do you think perhaps any other changes might take place as the planet warms from the CO2 that might invalidate the logarithmic relationship — like, maybe, a boiling away of the world’s oceans? Or just, in the beginning, a rise in water vapor pressure (due to CO2’s warming) that would cause a positive feedback — one we’re already starting to observe on Earth?

I explained this to you earlier — at least twice. Yet you blithely ignore any and all evidence you don’t want to hear, like a kid who puts his fingers in his ears and shouts “I can’t hear youuuuuuuuuuuu!”

I first encountered Chris Colose in 2010 during a discussion concerning Venus at “Science of Doom”. What little I know about “Climate Science” was learned at SOD from Leonard Weinstein and DeWitt Payne. It was DeWitt who introduced me to Rodrigo Caballero of University College, Dublin.

Chris quickly demonstrated that he is a young arrogant light weight. His simple faith in the powers of CO2 made him look foolish in the SOD discussion that is quite relevant to this thread. I hope you will take the time to look at it:http://scienceofdoom.com/2010/06/12/venusian-mysteries/

Peter, where is your missing energy?
—
It’s not clear — could you handle Colose’s math, or not?
Do you understand what a partial derivative is, or not?
It’s an important question. Please answer honestly.

Chris Colose says that if the energy balance is positive the Earth is going to heat up and if it is negative it will cool down. I can’t disagree with that but are we cooling down or warming up? He doesn’t say.

Yes, I do understand partial differentials. Also vector calculus (Div, Grad and Curl), tensors, spherical trigonometry, Hamiltonians, General Relativity and much more. When you build a 1 GeV electron synchrotron to drive a “Free Electron Laser” that uses Inverse Compton Scattering to generate the world’s brightest gamma ray beam things get a little weird and you had better believe what the equations tell you.

Electrons with 2,000 times their rest mass! Photon energies multiplied by 5,000,000:1! A photon with an energy of 2 eV transformed into a gamma ray with 10 MeV energy.

All that training in “Hard Science” makes it difficult for me to believe “Fairy Stories” from people like James Hansen and Gavin Schmidt.

On Venus 16,000 W/m2 leaves the surface but only 157 W/m2 is radiated from the cloud tops. My question is where does that imbalance come from rather than where it went, If you can explain it without using thermodynamics you win!

Back in 1905 Albert could not get a job in a university so he was employed as a lowly patent clerk. Even so he was able to publish four papers in 1905 in Annalen der Physik including his Special Theory of Relativity.

This speaks volumes about the openess of the peer review process one hundred years ago. How many of today’s prestigious peer reviewed journals would dare to publish a paper from a patent clerk?

Learn some history. Annalen der Physik was one of the premier journals in the world in Einstein’s time. He published his papers there like everyone else — by sending it to an editor for review.

Doug Cotton simply spams the Web with his junk, and is afraid to submit it to a real journal becaouse he knows it would be summarily rejected. Better to use a vanity press and maintain one’s illusion of superiority.

To summarize it seems you don’t accept the Arrhenius fantasy any more than I do. I see it as the proverbial fig leaf used to cover the abject nakedness of the “CAGW Scientists”.

We seem to agree that thermodynamics based on the major components of the atmosphere explains what is observed much better than theories that see everything in terms of trace components such as CO2 and water vapor.

We may disagree when it comes heat emanating from the interior of planets, I see this as a significant issue for the gas giants but not for rocky planets.

Why do they use the same albedo figure(clouds etc) when they calculate Earth greenhouse with or without atmosphere?
Without atmosphere there would be no clouds or snow?
The greenhouse effect is closer to less than half of 33 deg C?

Here are some estimates of what the Earth’s average temperature would be if it lacked atmosphere and oceans, taken from an earlier post on this site.

Scott Denning 255 K
This camel 156 K
Nikolov & Zeller 154 K

Nikolov & Zeller arrive at their temperature by saying that Earth would be at the same temperature as the Moon if it lacked any kind of atmosphere. Their 154 K is based on the Moon’s average temperature as measured by the Diviner Experiment.

I say that the average temperature should be slightly higher than N&K claim because the Earth rotates roughly 30 times faster than the Moon (relative to the Sun).

Denning’s figure would be mathematically correct if the entire surface of the Earth were at a constant temperature. On the Moon the temperature varies over a wide range according to the time of day and latitude. Why would an airless Earth be different?http://www.diviner.ucla.edu/science.shtml

Thus according to N&K (and this camel) the real GHE is ~130 K rather than the 33 K claimed by Scott Denning.

He — and it’s not him — this calculation was done long ago — simply assumes that the surface temperature of the Earth is constant, due to some method of equilibration such as an atmosphere.

Do you really not even understand this?

—
Peter, I am honestly trying here…. but your replies are getting so ridiculous that I cannot justify wasting much more time on this. You stubbornly cling to your ideas, despite all reason and all evidence.

That’s OK — I’m not one to dismiss practical hands-on experience, which I was never much good at myself. But I think honesty is required here, since you are opining far outside your field of laser building.

David Appell said:
“Physicists tend not to be very enamored with hypotheses that violate conservation of energy. I’m wondering why you are.”

I have made several attempts to explain your schoolboy “howler” (demanding an explanation for an imaginary energy imbalance of 150 W/m^2). Here is one more attempt, not so much for you (will you ever get it?) but for other people who may be confused by your erudition in voodoo science and dogma. All that follows can be referenced to the Kiehl-Trenberth energy balance diagram and Michael Mann’s modified single layer atmospheric model.

At the top of the atmosphere 240 W/m^2 is lost into space in the form of thermal IR radiation corresponding to a temperature of ~240 K. This outgoing radiation is balanced exactly by energy radiated back to Earth’s surface. The precision of this balance depends on the fact that there are no significant heat sinks at the cloud tops. This exact 50:50 split came up earlier in a discussion with “Mostly Harmless”:https://diggingintheclay.wordpress.com/2013/02/16/unified-theory-of-climate-revisited/#comment-4484

At the Earth’s surface the average incident energy is 390 W/m^2 mostly in the form of incoming solar radiation. The Earth’s surface emits about 390 W/m^2 upwards in the form of thermal IR radiation (corresponding to an average temperature of 288 K) but in this case the energy does not balance exactly owing to local heat sinks, the most significant of which are the oceans covering >70% of the planet. This unbalance is Trenberth’s “Missing Heat”. Well funded studies are ongoing on using the Argo buoys to quantify it.

So the 150 W/m^2 “Energy Imbalance” you keep talking about is just another way of saying that, on average, the cloud tops are cooler than the Earth’s surface.

Why not ask what makes the cloud tops are cooler than the surface? This is the measurable Greenhouse Effect. It is mainly due to the major gases in the atmosphere that dictate a temperature gradient of approximately -g/Cp throughout most of the troposphere. It follows that the temperature differential between the cloud tops and the surface is directly proportional to the depth of the troposphere which in turn is proportional to pressure.

It is the total atmospheric pressure that makes the surface of Venus so hot. It would make little difference if all the CO2 was replaced by an equal mass of Nitrogen. Carl Sagan did the calculations almost 50 years ago published in peer reviewed journals. N&K are trying to generalize what Sagan started.

While the GHE can be explained in terms of total atmosperic pressure it cannot be explained in terms of trace gases. Arrhenius and Hansen are simply wrong. Their theories don’t fit the facts.

The Earth’s surface emits about 390 W/m^2 upwards in the form of thermal IR radiation (corresponding to an average temperature of 288 K) but in this case the energy does not balance exactly owing to local heat sinks, the most significant of which are the oceans covering >70% of the planet. This unbalance is Trenberth’s “Missing Heat”.

Wrong. Also, laughably wrong.

Energy balances at all layers of the atmosphere, including the surface. Physicists call this “conservation of energy,” and it has no known exceptions, anywhere, ever. It is the most important principle in all of physics, and applies everywhere — no exceptions.

My degrees are in Physics and Electrical Engineering. I won a few awards and prizes in the process but don’t want to sound boastful.

If you live on the east side of USA, why not sign up for one of my courses? I hand out air freshener labeled “Bullshit Repellent” to my students and encourage them to use it if they think I have strayed from the path of truth or reason. You might be inclined to do that more than most students; the resulting discussions would be wonderful for improving everyone’s understanding.

Climate change is not a major interest for me. What I really care about is improving public education. Thus far I have helped create eight new schools in the USA including this one:http://www.woodscharter.org/

David Appell (@davidappell),
The intellectually bankrupt commonly resort to “ad hominem” attacks. If you want to do a hatchet job on my education and accomplishments you have enough clues already. Go for it and then explain why your opinion has such great value.

The real problem here is your amazing ability to misunderstand even high school physics. Surprisingly for someone who writes well, your reading comprehension is poor. For example how did you miss this:
“My degrees are in Physics and Electrical Engineering.”

Slow students are always a special challenge but I have the patience in spite of a heavy teaching load (the kind I get paid for) over the next few weeks. You can easily find out where but I don’t see that as relevant to this thread.

You were wrong when you stated:
“But think about this: their picture of an airless planetary body is one that has T= 0 at certain points on its surface — the points where the radiation comes in perpendicular to the surface, or on its nightside.”

Somehow you overlooked the Cs term in the equation which corresponds to the 2.7 K temperature of the universe.

However, if you had said the equation implies a planetary body made of a perfect insulator I might have agreed. The N&K equation contrasts with Scott Denning’s derivation of the 255 K surface temperature which implies a body made of a thermal superconductor. The correct answer is likely to fall between these two extremes.

As I pointed out in “Unified Theory of Climate Revisited”, N&K overlooked the effect of rotation. As the rate of rotation increases, temperature swings are reduced, so the average temperature rises. That means that an airless Earth with its 30 times greater rate of rotation would be warmer than the Moon. How much warmer? I don’t know enough about the thermal properties of the Moon (or an airless Earth) to calculate it so I made an outrageous guess (156 K).

Just for the record what is your figure for the average temperature of an airless Earth?

The N&K equation contrasts with Scott Denning’s derivation of the 255 K surface temperature which implies a body made of a thermal superconductor.

For the Nth time, it is not “Scott Denning’s derivation” — the formula has been around forever.

And the assumption has nothing to do with superconductivity of its surface. The assumption is a much more realistic one — that the planet’s atmosphere is in equilibrium at the same temperature, and that the atmosphere is gray.

You have mischaracterized and misapplied this formula, and to make it worse implied that I did, and until you correct these I will not discuss science with someone who can’t be honest about the simpliest things.

I recently read somewhere that Arrhenius himself Reduced his estimate of climate sensitivity, in 1906. And that he reduced it to something less than 2. But damned if I can find my way back to that article! And other articles I come across, saying nothing on the matter.

Otter,
In his 1896 paper Arrhenius claimed that what some call the “Sensitivity Constant” is 5.3 K/doubling of CO2. Angstrom disputed the Arrhenius theory and I was under the impression that this persuaded Arrhenius to reduce his sensitivity constant. However I have not been able to uncover any clear evidence for this!

As I explain above, it is not possible to choose a single value of sensitivity constant that fits observations over long periods of time. This proves that the Arrhenius hypothesis is false no matter how many “Scientists” say otherwise.

The IPCC amplified the myth that CO2 concentrations are a major factor in determining average global temperature. They did it by picking on the century following 1850 (SAR, 1995). In my opinion the striking correlation between the variables over this period is coincidental given that since peaking in 1998; in spite of the monotonic rise in CO2 concentrations, average global temperatures have stagnated since 1998. Looking forward, a downward trend seems just as likely as an upward one.

Galloping~ Thanks! I’ve done a (little) bit of searching myself on whether Arrhenius reduced his estimate, also with no luck. I did find a sentence (somewhere, should have kept the link!) claiming a reduction to 1.6C (2.1 C accounting for water vapor). But I believe even that site reported that it could not be verified.

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The elevation of the hockey stick and the whole global warming thing to iconic status makes it a giant with feet of clay – poorly founded and ready to crumble. Time to do some digging…